Preheat your oven to 350°F (175°C).
Remove the core from the cabbage and carefully peel away the leaves. Blanch the cabbage leaves in boiling water for about 5 minutes until softened. Drain and set aside.
In a large skillet, heat the olive oil or butter over medium heat. Add the diced onion and minced garlic, sautéing until the onion is translucent, about 4-5 minutes.
Add the ground beef or turkey to the skillet and cook until browned, breaking it up with a spoon. Drain excess fat if necessary.
Stir in the cooked rice, diced tomatoes (with juice), paprika, oregano, salt, and black pepper. Let the mixture simmer for about 5 minutes to combine the flavors.
In the casserole dish, layer half of the cabbage leaves at the bottom. Spoon half of the meat and rice mixture over the cabbage.
Add another layer of cabbage leaves followed by the remaining meat mixture. Top with the remaining cabbage leaves and sprinkle the shredded cheese evenly over the top.
Cover the casserole dish with foil and bake for 30 minutes. Remove the foil and bake for an additional 15 minutes, or until the cheese is bubbly and golden.
Allow the casserole to cool for a few minutes before serving.